## Special purpose computer for digital holographic particle tracking velocimetry

Optics Express, Vol. 14, Issue 2, pp. 587-592 (2006)

http://dx.doi.org/10.1364/OPEX.14.000587

Acrobat PDF (1077 KB)

### Abstract

We have designed a special purpose computer system for digital holographic particle tracking velocimetry (DHPTV). We present the pipeline for calculating the intensity of an object from a hologram by fast Fourier transform in an FPGA chip. This system uses four FPGA chips and can make 100 reconstructed images from a 256×256-grid hologram in 266 msec. It is expected that this system will improve the efficiency of analysis in DHPTV.

© 2006 Optical Society of America

## 1. Introduction

01. D.H. Barnhart, R.J. Adrian, and G.C. Papen,“Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. **33**, 7159–7170 (1994). [CrossRef] [PubMed]

02. H. Memg and F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. **34**, 1827–1840 (1995). [CrossRef]

03. J. Sheng, E. Malkiel, and J. Katz,“Single beam two-views holographic particle image velocimetry,” Appl. Opt. **42**, 235–250 (2003). [CrossRef] [PubMed]

04. U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. **33**, 179–181 (1994). [CrossRef] [PubMed]

05. S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. **32**, 567–574 (2000). [CrossRef]

04. U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. **33**, 179–181 (1994). [CrossRef] [PubMed]

05. S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. **32**, 567–574 (2000). [CrossRef]

07. T. Ito, T. Yabe, M. Ozaki, and M. Yanagi,“Special-purpose computer HORN-1 for reconstruction of virtual image in three dimensions,”Comp. Phys. Commun. **82**104–110 (1994). [CrossRef]

08. T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, “Special-purpose computer for holography HORN-2,” Comp. Phys. Commun. **93**13–20(1996). [CrossRef]

09. T. Shimobaba, N. Masuda, T. Sugie, S. Hosono, S. Tsukui, and T. Ito, “Special-purpose computer for holography HORN-3 with PLD technology,” Comp. Phys. Commun. **130**, 75–82(2002). [CrossRef]

10. T. Shimobaba and T. Ito, “Special-purpose computer for holography HORN-4 with recurrence algorithm,” Comp. Phys. Commun. **148**, 160–170(2002). [CrossRef]

11. T. Ito, K.N. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie “A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction,” Opt. Express , **13**, 1923–1932(2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1923 [CrossRef] [PubMed]

## 2. Algorithm of DHPTV

*x*,

_{i}*y*,

_{i}*Z*) is the amplitude of the object light at point (

_{i}*x*,

_{i}*y*,

_{i}*z*), λ is the wavelength of the reference light,

_{i}*I*is the intensity of the hologram at point (

_{α}*x*,

_{α}*y*, 0),

_{α}*k*is the wavenumber of the reference light, and

*N*is the number of division of the hologram grid in the x or y directions. Note that in Eq. (1), the hologram is on the

*z*= 0 plane. Furthermore, using the Fresnel approximation we obtain

*n*,

*m*) is the two-dimensional Fourier transform of ϕ(

*x*,

_{i}*y*,

_{i}*z*),

_{i}*I*̂(

*n*,

*m*) is the transform of

*I*, and

_{α}*G*(

*n*,

*m*) is the transform of

*g*(

*x*-

_{i}*x*,

_{α}*y*-

_{i}*y*).

_{α}*x*, Δ

_{α}*y*is the grid size of the hologram.

_{α}*z*-direction. Each plane is reconstructed keeping

*z*constant. To calculate Eq. (3), the method described below was contrived:

## 3. Hardware design

11. T. Ito, K.N. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie “A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction,” Opt. Express , **13**, 1923–1932(2005),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1923 [CrossRef] [PubMed]

## 4. Performance

## 5. Conclusion

## Acknowledgments

## References and links

01. | D.H. Barnhart, R.J. Adrian, and G.C. Papen,“Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. |

02. | H. Memg and F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. |

03. | J. Sheng, E. Malkiel, and J. Katz,“Single beam two-views holographic particle image velocimetry,” Appl. Opt. |

04. | U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. |

05. | S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. |

06. | S. Satake, T. Kunugi, K. Sato, and T. Ito, “Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel,” Opt. Rev. |

07. | T. Ito, T. Yabe, M. Ozaki, and M. Yanagi,“Special-purpose computer HORN-1 for reconstruction of virtual image in three dimensions,”Comp. Phys. Commun. |

08. | T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, “Special-purpose computer for holography HORN-2,” Comp. Phys. Commun. |

09. | T. Shimobaba, N. Masuda, T. Sugie, S. Hosono, S. Tsukui, and T. Ito, “Special-purpose computer for holography HORN-3 with PLD technology,” Comp. Phys. Commun. |

10. | T. Shimobaba and T. Ito, “Special-purpose computer for holography HORN-4 with recurrence algorithm,” Comp. Phys. Commun. |

11. | T. Ito, K.N. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie “A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction,” Opt. Express , |

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(120.7250) Instrumentation, measurement, and metrology : Velocimetry

**ToC Category:**

Holography

**Citation**

Nobuyuki Masuda, Tomoyoshi Ito, Kazuya Kayama, Hiroaki Kono, Shin-ichi Satake, Tomoaki Kunugi, and Kazuho Sato, "Special purpose computer for digital holographic particle tracking velocimetry," Opt. Express **14**, 587-592 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-587

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### References

- D.H.Barnhart, R.J.Adrian and G.C.Papen,"Phase-conjugate holographic system for high-resolution particle-image velocimetry," Appl. Opt. 33, 7159-7170 (1994). [CrossRef] [PubMed]
- H.Memg and F.Hussain, "In-line recording and off-axis viewing technique for holographic particle velocimetry," Appl. Opt. 34, 1827-1840 (1995). [CrossRef]
- J.Sheng, E.Malkiel and J.Katz,"Single beam two-views holographic particle image velocimetry," Appl. Opt. 42, 235-250 (2003). [CrossRef] [PubMed]
- U.Schnars, T. Kreis and W.Juptner, "Direct recording of holograms by CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
- S.Murata and N.Yasuda, "Potential of digitalholography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000). [CrossRef]
- S. Satake, T. Kunugi, K. Sato and T. Ito, "Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel," Opt. Rev. 11, 162-164 (2004).
- T. Ito, T. Yabe, M. Ozaki and M. Yanagi,"Special-purpose computer HORN-1 for reconstruction of virtual image in three dimensions,"Comp. Phys. Commun. 82 104-110 (1994). [CrossRef]
- T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93 13-20(1996). [CrossRef]
- T. Shimobaba, N. Masuda, T. Sugie, S. Hosono, S. Tsukui, and T. Ito, "Special-purpose computer for holography HORN-3 with PLD technology," Comp. Phys. Commun. 130, 75-82(2000). [CrossRef]
- T. Shimobaba, and T. Ito, "Special-purpose computer for holography HORN-4 with recurrence algorithm," Comp. Phys. Commun. 148, 160-170(2002). [CrossRef]
- T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba and T. Sugie "A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction," Opt. Express , 13, 1923-1932(2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1923">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1923</a> [CrossRef] [PubMed]

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